Supplementary Material of the paper entitled:

Causality of Genetically Determined Monounsaturated Fatty Acids on Risk of Cardiovascular Disease: A Mendelian Randomization Study

Authors list

1. Danial Habibi
   
2. Mahdi Akbarzadeh
3. Farshad Teymoori
4. Sahand Tehrani Fateh
5. Sajedeh Masjoudi
6. Amir Hossein Saeidian
7. Farhad Hosseinpanah
8. Noushin Mosavi
9. Hakon Hakonarson
10. Fereidoun Azizi
11. Alireza Soleymani T
12. Mehdi Hedayati
13. Maryam Sadat Daneshpour
14. Marjan Mansourian

• Abbreviations: (Follow tabs by these terms)
  • MUFA : Monounsaturated Fatty Acids
  • ANG : Angina - Chest Pain
  • ASCVD : Atherosclerotic Cardiovascular Diseases
  • IHD : Ischemic heart disease
  • MI : Myocardial Infarction
  • HTN : Hypertension
  • CVD : Cardiovascular Disease

[ANG]

Introduction

• Title: Investigating the causality between Monounsaturated Fatty Acids on Cardiovascular Disease

  • Exposure: Monounsaturated Fatty Acids, Data downloaded from IEU OpenGWAS project Database | ID: ukb-b-8468
  • Sample size: 461,880
  • Outcome: Angina, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-b-8468
  • Sample size: 461,880 , Number of cases: 14,828 , Number of controls: 447,052
    
  • Ancestry: European
  • Outcome: Atherosclerotic, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-b-1668
  • Sample size: 463,010 , Number of cases: 12,171 , Number of controls: 450,839
    
  • Ancestry: European
  • Outcome: Ischemic heart disease, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-d-I9_IHD
  • Sample size: 361,194 , Number of cases: 20,857 , Number of controls: 340,337
    
  • Ancestry: European
  • Outcome: Myocardial infarction, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-b-15829
  • Sample size: 462,933 , Number of cases: 10,616 , Number of controls: 452,317
    
  • Ancestry: European
  • Outcome: High blood pressure, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-b-14177
  • Sample size: 461,880 , Number of cases: 124,227 , Number of controls: 337,653
    
  • Ancestry: European

Data Preparation

1- Number of total SNPs in exposure: 12,321,875 SNPs

2- Number of Selected SNPs exposure: 44 SNPs

3- Number of total SNPs in outcome: 9,851,867 SNPs

4- Number of common variants between exposure and outcome: 37 SNPs

5- Number of SNPs after harmonization (action=2) = 36 SNPs

6- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 36 SNPs

7- Number of SNPs after removing those that have MAF < 0.01 = 36 SNPs

8- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 4 SNPs (rs115849089, rs1260326, rs429358, and rs56289821)

Checking weakness of the instruments

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   21.29   22.20   24.82   29.35   27.70   81.06

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

Initial MR analysis

id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
w10boa	0DIRXV	outcome	exposure	MR Egger	32	0.0092767	0.0035303	0.0134136
w10boa	0DIRXV	outcome	exposure	Weighted median	32	0.0045031	0.0014980	0.0026468
w10boa	0DIRXV	outcome	exposure	Inverse variance weighted	32	0.0043228	0.0012409	0.0004945
w10boa	0DIRXV	outcome	exposure	Simple mode	32	0.0085288	0.0032231	0.0126736
w10boa	0DIRXV	outcome	exposure	Weighted mode	32	0.0076863	0.0030941	0.0185940

Heterogeneity testing

id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
w10boa	0DIRXV	outcome	exposure	MR Egger	47.16615	30	0.0239700
w10boa	0DIRXV	outcome	exposure	Inverse variance weighted	50.67952	31	0.0143121

pleiotropy testing

id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
w10boa	0DIRXV	outcome	exposure	-0.0004509	0.0003016	0.1453901

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate         Sd   T-stat
## 1 beta.exposure               Raw     0.004322811 0.00124086 3.483722
## 2 beta.exposure Outlier-corrected              NA         NA       NA
##       P-value
## 1 0.001496903
## 2          NA
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 54.70446
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.015
## 
## 
## $`MR-PRESSO results`$`Outlier Test`
##          RSSobs Pvalue
## 1  8.029625e-07  0.672
## 2  1.684675e-07      1
## 3  1.924740e-07      1
## 4  1.843632e-07      1
## 5  1.225485e-07      1
## 6  2.368531e-07      1
## 7  2.508848e-07      1
## 8  1.021119e-07      1
## 9  2.426335e-07      1
## 10 1.662435e-07      1
## 11 1.308346e-06      1
## 12 5.904347e-08      1
## 13 9.220546e-07  0.576
## 14 1.009905e-07      1
## 15 6.716404e-07      1
## 16 1.390861e-07      1
## 17 7.805953e-09      1
## 18 8.297846e-07      1
## 19 6.893822e-09      1
## 20 2.248506e-07      1
## 21 1.210955e-07      1
## 22 4.142234e-11      1
## 23 2.921072e-08      1
## 24 1.885866e-08      1
## 25 7.331039e-07      1
## 26 7.803325e-06  0.096
## 27 2.196524e-07      1
## 28 4.488497e-09      1
## 29 3.509989e-08      1
## 30 9.982133e-07      1
## 31 1.658861e-07      1
## 32 2.712064e-06   0.16
## 
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] "No significant outliers"
## 
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## [1] NA
## 
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] NA

## [1] "One SNP (rs591592) were detected by MRPRESSO and excluded for further analyses"

MR analysis after excluding SNPs detected by MRPRESSO

id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
w10boa	0DIRXV	outcome	exposure	MR Egger	31	0.0090637	0.0036205	0.0181807
w10boa	0DIRXV	outcome	exposure	Weighted median	31	0.0047626	0.0015305	0.0018600
w10boa	0DIRXV	outcome	exposure	Inverse variance weighted	31	0.0044562	0.0012662	0.0004325
w10boa	0DIRXV	outcome	exposure	Simple mode	31	0.0085243	0.0032072	0.0124861
w10boa	0DIRXV	outcome	exposure	Weighted mode	31	0.0076822	0.0030292	0.0166527

Heterogeneity testing

id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
w10boa	0DIRXV	outcome	exposure	MR Egger	46.90949	29	0.0190151
w10boa	0DIRXV	outcome	exposure	Inverse variance weighted	49.88295	30	0.0127539

pleiotropy testing

id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
w10boa	0DIRXV	outcome	exposure	-0.0004244	0.000313	0.1856232

Radial test

## 
## Radial IVW
## 
##                     Estimate    Std.Error  t value     Pr(>|t|)
## Effect (Mod.2nd) 0.004329998 0.0012410857 3.488879 4.850506e-04
## Iterative        0.004329998 0.0012410857 3.488879 4.850506e-04
## Exact (FE)       0.004577654 0.0009823369 4.659964 3.162650e-06
## Exact (RE)       0.004498928 0.0013155902 3.419703 1.775749e-03
## 
## 
## Residual standard error: 1.265 on 31 degrees of freedom
## 
## F-statistic: 12.17 on 1 and 31 DF, p-value: 0.00148
## Q-Statistic for heterogeneity: 49.61039 on 31 DF , p-value: 0.01832529
## 
##  No significant outliers 
## Number of iterations = 2

## [1] "No significant outliers"

## [1] "One SNP (rs964184) were detected by Radial and excluded for further analyses"

MR analysis after excluding SNPs detected by MRPRESSO

id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
w10boa	0DIRXV	outcome	exposure	MR Egger	31	0.0064702	0.0035991	0.0826389
w10boa	0DIRXV	outcome	exposure	Weighted median	31	0.0036906	0.0015056	0.0142386
w10boa	0DIRXV	outcome	exposure	Inverse variance weighted	31	0.0035168	0.0011925	0.0031864
w10boa	0DIRXV	outcome	exposure	Simple mode	31	0.0083347	0.0031966	0.0140789
w10boa	0DIRXV	outcome	exposure	Weighted mode	31	0.0074323	0.0030396	0.0205665

Heterogeneity testing

id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
w10boa	0DIRXV	outcome	exposure	MR Egger	40.90141	29	0.0702423
w10boa	0DIRXV	outcome	exposure	Inverse variance weighted	41.96936	30	0.0720070

pleiotropy testing

id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
w10boa	0DIRXV	outcome	exposure	-0.0002607	0.0002996	0.3913518

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Refernce

Run After deleting new outlier: Final Results:

MR analysis after deleting outliers

id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
w10boa	0DIRXV	outcome	exposure	MR Egger	25	0.0080165	0.0034233	0.0282202
w10boa	0DIRXV	outcome	exposure	Weighted median	25	0.0063587	0.0016061	0.0000752
w10boa	0DIRXV	outcome	exposure	Inverse variance weighted	25	0.0050631	0.0011313	0.0000076
w10boa	0DIRXV	outcome	exposure	Simple mode	25	0.0087734	0.0029586	0.0067373
w10boa	0DIRXV	outcome	exposure	Weighted mode	25	0.0082151	0.0027323	0.0061073

Heterogeneity testing

id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
w10boa	0DIRXV	outcome	exposure	MR Egger	17.81368	23	0.7675161
w10boa	0DIRXV	outcome	exposure	Inverse variance weighted	18.64924	24	0.7704279

pleiotropy testing

id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
w10boa	0DIRXV	outcome	exposure	-0.0002564	0.0002806	0.3701534

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 28 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     IVW    0.005     0.001 0.003, 0.007   0.000
## ------------------------------------------------------------------
## Residual standard error =  0.911 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 22.3877 on 27 degrees of freedom, (p-value = 0.7174). I^2 = 0.0%.

##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.006     0.002   0.003 0.009   0.000
##            Weighted median    0.006     0.002   0.003 0.009   0.000
##  Penalized weighted median    0.006     0.002   0.004 0.009   0.000
##                                                                    
##                        IVW    0.005     0.001   0.003 0.007   0.000
##              Penalized IVW    0.005     0.001   0.003 0.007   0.000
##                 Robust IVW    0.005     0.001   0.003 0.007   0.000
##       Penalized robust IVW    0.005     0.001   0.003 0.007   0.000
##                                                                    
##                   MR-Egger    0.008     0.003   0.002 0.014   0.009
##                (intercept)    0.000     0.000  -0.001 0.000   0.279
##         Penalized MR-Egger    0.008     0.003   0.002 0.014   0.009
##                (intercept)    0.000     0.000  -0.001 0.000   0.279
##            Robust MR-Egger    0.008     0.003   0.001 0.015   0.019
##                (intercept)    0.000     0.000  -0.001 0.000   0.355
##  Penalized robust MR-Egger    0.008     0.003   0.001 0.015   0.019
##                (intercept)    0.000     0.000  -0.001 0.000   0.355

id.exposure	id.outcome	exposure	outcome	snp_r2.exposure	snp_r2.outcome	correct_causal_direction	steiger_pval
w10boa	0DIRXV	exposure	outcome	0.001838	8.94e-05	TRUE	0

## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] 0.005121877
## 
## $beta.se
## [1] 0.00112464
## 
## $beta.p.value
## [1] 5.257628e-06
## 
## $naive.se
## [1] 0.001104662
## 
## $chi.sq.test
## [1] 21.74294

##   over.dispersion loss.function    beta.hat     beta.se
## 1           FALSE            l2 0.005121877 0.001124640
## 2           FALSE         huber 0.005279650 0.001156012
## 3           FALSE         tukey 0.005289270 0.001156148
## 4            TRUE            l2 0.005136566 0.001147648
## 5            TRUE         huber 0.005278331 0.001157411
## 6            TRUE         tukey 0.005289602 0.001157629

## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  28 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.005 0.001  0.000 [0.003,0.007]
## ------------------------------------------------------------------

## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 28 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value Condition
##    dIVW    0.005     0.001 0.003, 0.007   0.000   142.585
## ------------------------------------------------------------------

## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 28 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     MBE    0.008     0.003 0.003, 0.013   0.002
## ------------------------------------------------------------------

[ASCVD]

Introduction

• Title: Investigating the causality between Monounsaturated Fatty Acids on Cardiovascular Disease

  • Exposure: Monounsaturated Fatty Acids, Data downloaded from IEU OpenGWAS project Database | ID: ukb-b-8468
  • Sample size: 461,880
  • Outcome: Angina, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-b-8468
  • Sample size: 461,880 , Number of cases: 14,828 , Number of controls: 447,052
    
  • Ancestry: European
  • Outcome: Atherosclerotic, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-b-1668
  • Sample size: 463,010 , Number of cases: 12,171 , Number of controls: 450,839
    
  • Ancestry: European
  • Outcome: Ischemic heart disease, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-d-I9_IHD
  • Sample size: 361,194 , Number of cases: 20,857 , Number of controls: 340,337
    
  • Ancestry: European
  • Outcome: Myocardial infarction, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-b-15829
  • Sample size: 462,933 , Number of cases: 10,616 , Number of controls: 452,317
    
  • Ancestry: European
  • Outcome: High blood pressure, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-b-14177
  • Sample size: 461,880 , Number of cases: 124,227 , Number of controls: 337,653
    
  • Ancestry: European

Data Preparation

1- Number of total SNPs in exposure: 12,321,875 SNPs

2- Number of Selected SNPs exposure: 44 SNPs

3- Number of total SNPs in outcome: 9,851,867 SNPs

4- Number of common variants between exposure and outcome: 36 SNPs

5- Number of SNPs after harmonization (action=2) = 35 SNPs

6- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 35 SNPs

7- Number of SNPs after removing those that have MAF < 0.01 = 35 SNPs

8- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 0 SNPs

Checking weakness of the instruments

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   21.34   22.36   24.96   31.10   30.73   86.31

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

Initial MR analysis

id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
Ae0Nt5	TcYOpY	outcome	exposure	MR Egger	35	0.0109733	0.0049384	0.0332498
Ae0Nt5	TcYOpY	outcome	exposure	Weighted median	35	0.0044997	0.0012533	0.0003304
Ae0Nt5	TcYOpY	outcome	exposure	Inverse variance weighted	35	0.0057876	0.0016046	0.0003098
Ae0Nt5	TcYOpY	outcome	exposure	Simple mode	35	0.0041996	0.0026274	0.1192024
Ae0Nt5	TcYOpY	outcome	exposure	Weighted mode	35	0.0065586	0.0020791	0.0033544

Heterogeneity testing

id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
Ae0Nt5	TcYOpY	outcome	exposure	MR Egger	126.6698	33	0
Ae0Nt5	TcYOpY	outcome	exposure	Inverse variance weighted	131.3981	34	0

pleiotropy testing

id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
Ae0Nt5	TcYOpY	outcome	exposure	-0.0004771	0.0004298	0.2750741

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate           Sd   T-stat
## 1 beta.exposure               Raw     0.005787622 0.0016045628 3.606978
## 2 beta.exposure Outlier-corrected     0.004639196 0.0009916789 4.678123
##        P-value
## 1 9.827571e-04
## 2 5.392219e-05
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 138.0242
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] "<0.001"
## 
## 
## $`MR-PRESSO results`$`Outlier Test`
##          RSSobs Pvalue
## 1  1.521081e-07      1
## 2  5.817698e-07      1
## 3  1.009412e-06      1
## 4  2.417938e-08      1
## 5  2.405264e-07      1
## 6  6.280592e-08      1
## 7  1.860700e-07      1
## 8  3.020725e-09      1
## 9  3.419849e-07      1
## 10 3.559686e-07      1
## 11 9.105534e-08      1
## 12 6.135183e-08      1
## 13 1.624695e-07      1
## 14 6.151788e-07      1
## 15 1.221771e-06  0.105
## 16 6.157827e-08      1
## 17 1.439327e-06 <0.035
## 18 1.753513e-07      1
## 19 3.837921e-08      1
## 20 3.905884e-06      1
## 21 9.285519e-06 <0.035
## 22 2.051024e-08      1
## 23 8.867844e-06 <0.035
## 24 4.106314e-08      1
## 25 6.460918e-08      1
## 26 3.992742e-09      1
## 27 2.082157e-07      1
## 28 1.062721e-07      1
## 29 1.867962e-06      1
## 30 1.306280e-07      1
## 31 6.780487e-08      1
## 32 4.822383e-08      1
## 33 2.477448e-07      1
## 34 2.927522e-07      1
## 35 1.914666e-07      1
## 
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 17 21 23
## 
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure 
##      24.75486 
## 
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.118

## [1] "Four SNPs (rs59014134, rs75117471, rs115849089, and rs17092642) were detected by MRPRESSO and excluded for further analyses"

MR analysis after excluding SNPs detected by MRPRESSO

id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
Ae0Nt5	TcYOpY	outcome	exposure	MR Egger	31	0.0104860	0.0054383	0.0636786
Ae0Nt5	TcYOpY	outcome	exposure	Weighted median	31	0.0044096	0.0013655	0.0012407
Ae0Nt5	TcYOpY	outcome	exposure	Inverse variance weighted	31	0.0056432	0.0017519	0.0012771
Ae0Nt5	TcYOpY	outcome	exposure	Simple mode	31	0.0039667	0.0027647	0.1616979
Ae0Nt5	TcYOpY	outcome	exposure	Weighted mode	31	0.0063459	0.0020183	0.0037375

Heterogeneity testing

id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
Ae0Nt5	TcYOpY	outcome	exposure	MR Egger	121.6015	29	0
Ae0Nt5	TcYOpY	outcome	exposure	Inverse variance weighted	125.3132	30	0

pleiotropy testing

id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
Ae0Nt5	TcYOpY	outcome	exposure	-0.0004444	0.0004723	0.3545535

Radial test

## 
## Radial IVW
## 
##                     Estimate    Std.Error  t value     Pr(>|t|)
## Effect (Mod.2nd) 0.005791559 0.0016047538 3.609002 3.073776e-04
## Iterative        0.005791559 0.0016047538 3.609002 3.073776e-04
## Exact (FE)       0.006560284 0.0008407593 7.802808 6.054467e-15
## Exact (RE)       0.005996549 0.0015560471 3.853706 4.914767e-04
## 
## 
## Residual standard error: 1.921 on 34 degrees of freedom
## 
## F-statistic: 13.02 on 1 and 34 DF, p-value: 0.000977
## Q-Statistic for heterogeneity: 125.4644 on 34 DF , p-value: 2.088556e-12
## 
##  Outliers detected 
## Number of iterations = 2

##          SNP Q_statistic      p.value
## 1  rs2642636    11.60042 6.593689e-04
## 2   rs429358    40.64017 1.830054e-10
## 3 rs56289821    30.63685 3.111276e-08

## [1] "Three SNPs (rs2642636, rs429358, and rs56289821) were detected by Radial and excluded for further analyses"

MR analysis after excluding SNPs detected by MRPRESSO

id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
Ae0Nt5	TcYOpY	outcome	exposure	MR Egger	32	0.0087907	0.0029480	0.0056400
Ae0Nt5	TcYOpY	outcome	exposure	Weighted median	32	0.0045552	0.0012944	0.0004327
Ae0Nt5	TcYOpY	outcome	exposure	Inverse variance weighted	32	0.0046392	0.0009917	0.0000029
Ae0Nt5	TcYOpY	outcome	exposure	Simple mode	32	0.0028732	0.0029038	0.3300998
Ae0Nt5	TcYOpY	outcome	exposure	Weighted mode	32	0.0075955	0.0023215	0.0026235

Heterogeneity testing

id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
Ae0Nt5	TcYOpY	outcome	exposure	MR Egger	39.76543	30	0.1094881
Ae0Nt5	TcYOpY	outcome	exposure	Inverse variance weighted	42.71531	31	0.0784330

pleiotropy testing

id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
Ae0Nt5	TcYOpY	outcome	exposure	-0.0003872	0.0002596	0.1461938

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Refernce

Run After deleting new outlier: Final Results:

MR analysis after deleting outliers

id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
Ae0Nt5	TcYOpY	outcome	exposure	MR Egger	32	0.0087907	0.0029480	0.0056400
Ae0Nt5	TcYOpY	outcome	exposure	Weighted median	32	0.0045552	0.0012803	0.0003739
Ae0Nt5	TcYOpY	outcome	exposure	Inverse variance weighted	32	0.0046392	0.0009917	0.0000029
Ae0Nt5	TcYOpY	outcome	exposure	Simple mode	32	0.0028732	0.0030813	0.3582952
Ae0Nt5	TcYOpY	outcome	exposure	Weighted mode	32	0.0075955	0.0022451	0.0019571

Heterogeneity testing

id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
Ae0Nt5	TcYOpY	outcome	exposure	MR Egger	39.76543	30	0.1094881
Ae0Nt5	TcYOpY	outcome	exposure	Inverse variance weighted	42.71531	31	0.0784330

pleiotropy testing

id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
Ae0Nt5	TcYOpY	outcome	exposure	-0.0003872	0.0002596	0.1461938

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 32 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     IVW    0.005     0.001 0.003, 0.007   0.000
## ------------------------------------------------------------------
## Residual standard error =  1.174 
## Heterogeneity test statistic (Cochran's Q) = 42.7153 on 31 degrees of freedom, (p-value = 0.0784). I^2 = 27.4%.

##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.003     0.001   0.000 0.006   0.022
##            Weighted median    0.005     0.001   0.003 0.008   0.000
##  Penalized weighted median    0.006     0.001   0.004 0.009   0.000
##                                                                    
##                        IVW    0.005     0.001   0.003 0.007   0.000
##              Penalized IVW    0.005     0.001   0.003 0.007   0.000
##                 Robust IVW    0.005     0.001   0.003 0.007   0.000
##       Penalized robust IVW    0.005     0.001   0.003 0.007   0.000
##                                                                    
##                   MR-Egger    0.009     0.003   0.003 0.015   0.003
##                (intercept)    0.000     0.000  -0.001 0.000   0.136
##         Penalized MR-Egger    0.009     0.003   0.003 0.015   0.003
##                (intercept)    0.000     0.000  -0.001 0.000   0.136
##            Robust MR-Egger    0.009     0.003   0.003 0.016   0.006
##                (intercept)    0.000     0.000  -0.001 0.000   0.159
##  Penalized robust MR-Egger    0.009     0.003   0.003 0.016   0.006
##                (intercept)    0.000     0.000  -0.001 0.000   0.159

id.exposure	id.outcome	exposure	outcome	snp_r2.exposure	snp_r2.outcome	correct_causal_direction	steiger_pval
Ae0Nt5	TcYOpY	exposure	outcome	0.0023928	0.0001476	TRUE	0

## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] 0.00484049
## 
## $beta.se
## [1] 0.000882532
## 
## $beta.p.value
## [1] 4.139957e-08
## 
## $naive.se
## [1] 0.0008690899
## 
## $chi.sq.test
## [1] 41.4272

##   over.dispersion loss.function    beta.hat      beta.se
## 1           FALSE            l2 0.004840490 0.0008825320
## 2           FALSE         huber 0.004956247 0.0009068622
## 3           FALSE         tukey 0.004999124 0.0009073923
## 4            TRUE            l2 0.004789447 0.0010042786
## 5            TRUE         huber 0.004852868 0.0010587245
## 6            TRUE         tukey 0.004864635 0.0010644772

## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  32 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.005 0.001  0.000 [0.003,0.007]
## ------------------------------------------------------------------

## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 32 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value Condition
##    dIVW    0.005     0.001 0.003, 0.007   0.000   174.427
## ------------------------------------------------------------------

## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 32 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     MBE    0.008     0.002 0.003, 0.012   0.000
## ------------------------------------------------------------------

[IHD]

Introduction

• Title: Investigating the causality between Monounsaturated Fatty Acids on Cardiovascular Disease

  • Exposure: Monounsaturated Fatty Acids, Data downloaded from IEU OpenGWAS project Database | ID: ukb-b-8468
  • Sample size: 461,880
  • Outcome: Angina, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-b-8468
  • Sample size: 461,880 , Number of cases: 14,828 , Number of controls: 447,052
    
  • Ancestry: European
  • Outcome: Atherosclerotic, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-b-1668
  • Sample size: 463,010 , Number of cases: 12,171 , Number of controls: 450,839
    
  • Ancestry: European
  • Outcome: Ischemic heart disease, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-d-I9_IHD
  • Sample size: 361,194 , Number of cases: 20,857 , Number of controls: 340,337
    
  • Ancestry: European
  • Outcome: Myocardial infarction, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-b-15829
  • Sample size: 462,933 , Number of cases: 10,616 , Number of controls: 452,317
    
  • Ancestry: European
  • Outcome: High blood pressure, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-b-14177
  • Sample size: 461,880 , Number of cases: 124,227 , Number of controls: 337,653
    
  • Ancestry: European

Data Preparation

1- Number of total SNPs in exposure: 12,321,875 SNPs

2- Number of Selected SNPs exposure: 44 SNPs

3- Number of total SNPs in outcome: 13,586,589 SNPs

4- Number of common variants between exposure and outcome: 44 SNPs

5- Number of SNPs after harmonization (action=2) = 42 SNPs

6- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 42 SNPs

7- Number of SNPs after removing those that have MAF < 0.01 = 42 SNPs

8- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 4 SNPs (rs429358, rs56289821, and rs964184)

Checking weakness of the instruments

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   21.29   22.20   24.82   29.35   27.70   81.06

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

Initial MR analysis

id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
AyPdJL	f31Mp6	outcome	exposure	MR Egger	39	0.0050467	0.0044966	0.2689503
AyPdJL	f31Mp6	outcome	exposure	Weighted median	39	0.0041414	0.0021303	0.0518906
AyPdJL	f31Mp6	outcome	exposure	Inverse variance weighted	39	0.0063470	0.0017815	0.0003671
AyPdJL	f31Mp6	outcome	exposure	Simple mode	39	0.0002188	0.0045634	0.9620027
AyPdJL	f31Mp6	outcome	exposure	Weighted mode	39	0.0003692	0.0049426	0.9408443

Heterogeneity testing

id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
AyPdJL	f31Mp6	outcome	exposure	MR Egger	73.64755	37	0.0003178
AyPdJL	f31Mp6	outcome	exposure	Inverse variance weighted	73.84589	38	0.0004383

pleiotropy testing

id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
AyPdJL	f31Mp6	outcome	exposure	0.0001302	0.0004124	0.7540298

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate          Sd   T-stat
## 1 beta.exposure               Raw     0.006346974 0.001781519 3.562676
## 2 beta.exposure Outlier-corrected     0.005401467 0.001630537 3.312691
##       P-value
## 1 0.001008592
## 2 0.002072496
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 78.32892
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] "<0.001"
## 
## 
## $`MR-PRESSO results`$`Outlier Test`
##          RSSobs Pvalue
## 1  7.589045e-09      1
## 2  1.520959e-07      1
## 3  1.195763e-05      1
## 4  1.151350e-05 <0.039
## 5  1.315259e-05      1
## 6  1.829718e-08      1
## 7  3.177484e-06  0.546
## 8  7.762960e-07      1
## 9  2.255390e-07      1
## 10 6.914358e-07      1
## 11 6.033486e-07      1
## 12 2.501580e-07      1
## 13 1.045150e-06      1
## 14 3.219794e-05      1
## 15 2.531421e-06  0.117
## 16 1.119834e-06      1
## 17 1.536286e-07      1
## 18 2.737095e-07      1
## 19 1.442225e-06      1
## 20 1.196424e-06      1
## 21 1.358017e-08      1
## 22 8.712847e-07      1
## 23 5.256833e-07      1
## 24 1.713336e-08      1
## 25 8.242892e-06      1
## 26 1.273851e-07      1
## 27 2.723757e-06      1
## 28 2.269390e-06  0.702
## 29 7.465580e-08      1
## 30 1.582110e-07      1
## 31 6.197990e-08      1
## 32 2.102623e-07      1
## 33 4.351909e-06      1
## 34 3.165556e-06      1
## 35 1.212979e-06      1
## 36 3.320494e-06      1
## 37 1.093058e-07      1
## 38 1.275663e-07      1
## 39 6.704272e-07      1
## 
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 4
## 
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure 
##      17.50465 
## 
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.471

## [1] "One SNP (rs115849089) were detected by MRPRESSO and excluded for further analyses"

MR analysis after excluding SNPs detected by MRPRESSO

id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
AyPdJL	f31Mp6	outcome	exposure	MR Egger	38	0.0032148	0.0040745	0.4352741
AyPdJL	f31Mp6	outcome	exposure	Weighted median	38	0.0040640	0.0021087	0.0539520
AyPdJL	f31Mp6	outcome	exposure	Inverse variance weighted	38	0.0054015	0.0016305	0.0009240
AyPdJL	f31Mp6	outcome	exposure	Simple mode	38	0.0003045	0.0045716	0.9472453
AyPdJL	f31Mp6	outcome	exposure	Weighted mode	38	0.0004557	0.0052850	0.9317594

Heterogeneity testing

id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
AyPdJL	f31Mp6	outcome	exposure	MR Egger	57.64511	36	0.0124632
AyPdJL	f31Mp6	outcome	exposure	Inverse variance weighted	58.19616	37	0.0145811

pleiotropy testing

id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
AyPdJL	f31Mp6	outcome	exposure	0.0002176	0.0003709	0.5611136

Radial test

## 
## Radial IVW
## 
##                     Estimate   Std.Error  t value     Pr(>|t|)
## Effect (Mod.2nd) 0.006372348 0.001783352 3.573243 3.525878e-04
## Iterative        0.006372348 0.001783352 3.573243 3.525878e-04
## Exact (FE)       0.006807760 0.001295684 5.254183 1.486830e-07
## Exact (RE)       0.006573021 0.001994518 3.295543 2.134160e-03
## 
## 
## Residual standard error: 1.379 on 38 degrees of freedom
## 
## F-statistic: 12.77 on 1 and 38 DF, p-value: 0.000979
## Q-Statistic for heterogeneity: 72.24359 on 38 DF , p-value: 0.000669887
## 
##  Outliers detected 
## Number of iterations = 2

##           SNP Q_statistic      p.value
## 1 rs115849089    14.75908 0.0001221577

## [1] "One SNP (rs115849089) were detected by Radial and excluded for further analyses"

MR analysis after excluding SNPs detected by MRPRESSO

id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
AyPdJL	f31Mp6	outcome	exposure	MR Egger	38	0.0032148	0.0040745	0.4352741
AyPdJL	f31Mp6	outcome	exposure	Weighted median	38	0.0040640	0.0020613	0.0486539
AyPdJL	f31Mp6	outcome	exposure	Inverse variance weighted	38	0.0054015	0.0016305	0.0009240
AyPdJL	f31Mp6	outcome	exposure	Simple mode	38	0.0003045	0.0045575	0.9470827
AyPdJL	f31Mp6	outcome	exposure	Weighted mode	38	0.0004557	0.0047734	0.9244664

Heterogeneity testing

id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
AyPdJL	f31Mp6	outcome	exposure	MR Egger	57.64511	36	0.0124632
AyPdJL	f31Mp6	outcome	exposure	Inverse variance weighted	58.19616	37	0.0145811

pleiotropy testing

id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
AyPdJL	f31Mp6	outcome	exposure	0.0002176	0.0003709	0.5611136

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Refernce

Run After deleting new outlier: Final Results:

MR analysis after deleting outliers

id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
AyPdJL	f31Mp6	outcome	exposure	MR Egger	36	0.0034307	0.0036092	0.3485341
AyPdJL	f31Mp6	outcome	exposure	Weighted median	36	0.0029611	0.0021228	0.1630418
AyPdJL	f31Mp6	outcome	exposure	Inverse variance weighted	36	0.0041525	0.0014793	0.0049989
AyPdJL	f31Mp6	outcome	exposure	Simple mode	36	0.0000657	0.0046212	0.9887343
AyPdJL	f31Mp6	outcome	exposure	Weighted mode	36	0.0002129	0.0050532	0.9666373

Heterogeneity testing

id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
AyPdJL	f31Mp6	outcome	exposure	MR Egger	42.69331	34	0.1456808
AyPdJL	f31Mp6	outcome	exposure	Inverse variance weighted	42.75402	35	0.1724731

pleiotropy testing

id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
AyPdJL	f31Mp6	outcome	exposure	7.28e-05	0.0003312	0.8272782

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 36 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     IVW    0.004     0.001 0.001, 0.007   0.005
## ------------------------------------------------------------------
## Residual standard error =  1.105 
## Heterogeneity test statistic (Cochran's Q) = 42.7540 on 35 degrees of freedom, (p-value = 0.1725). I^2 = 18.1%.

##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.002     0.002  -0.002 0.006   0.306
##            Weighted median    0.004     0.002   0.000 0.008   0.070
##  Penalized weighted median    0.003     0.002  -0.001 0.007   0.195
##                                                                    
##                        IVW    0.004     0.001   0.001 0.007   0.005
##              Penalized IVW    0.004     0.001   0.001 0.007   0.005
##                 Robust IVW    0.004     0.002   0.000 0.007   0.036
##       Penalized robust IVW    0.004     0.002   0.000 0.007   0.036
##                                                                    
##                   MR-Egger    0.003     0.004  -0.004 0.011   0.342
##                (intercept)    0.000     0.000  -0.001 0.001   0.826
##         Penalized MR-Egger    0.003     0.004  -0.004 0.011   0.342
##                (intercept)    0.000     0.000  -0.001 0.001   0.826
##            Robust MR-Egger    0.003     0.004  -0.006 0.011   0.532
##                (intercept)    0.000     0.000  -0.001 0.001   0.756
##  Penalized robust MR-Egger    0.003     0.004  -0.006 0.011   0.532
##                (intercept)    0.000     0.000  -0.001 0.001   0.756

id.exposure	id.outcome	exposure	outcome	snp_r2.exposure	snp_r2.outcome	correct_causal_direction	steiger_pval
AyPdJL	f31Mp6	exposure	outcome	0.0024037	0.0001059	TRUE	0

## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] 0.004338291
## 
## $beta.se
## [1] 0.001395069
## 
## $beta.p.value
## [1] 0.001872575
## 
## $naive.se
## [1] 0.001370345
## 
## $chi.sq.test
## [1] 42.34696

##   over.dispersion loss.function    beta.hat     beta.se
## 1           FALSE            l2 0.004338291 0.001395069
## 2           FALSE         huber 0.003551043 0.001425995
## 3           FALSE         tukey 0.003792444 0.001427516
## 4            TRUE            l2 0.004144624 0.001487892
## 5            TRUE         huber 0.003407176 0.001580644
## 6            TRUE         tukey 0.003600889 0.001589118

## 
## MR-Lasso method 
## 
## Number of variants : 36 
## Number of valid instruments : 33 
## Tuning parameter : 0.3418043 
## ------------------------------------------------------------------
##  Exposure Estimate Std Error  95% CI       p-value
##  exposure    0.002     0.001 -0.001, 0.005   0.197
## ------------------------------------------------------------------

## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  36 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.004 0.001  0.002 [0.002,0.007]
## ------------------------------------------------------------------

## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 36 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value Condition
##    dIVW    0.004     0.002 0.001, 0.007   0.005   164.553
## ------------------------------------------------------------------

## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 36 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE    0.000     0.005 -0.010, 0.011   0.968
## ------------------------------------------------------------------

[MI]

Introduction

• Title: Investigating the causality between Monounsaturated Fatty Acids on Cardiovascular Disease

  • Exposure: Monounsaturated Fatty Acids, Data downloaded from IEU OpenGWAS project Database | ID: ukb-b-8468
  • Sample size: 461,880
  • Outcome: Angina, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-b-8468
  • Sample size: 461,880 , Number of cases: 14,828 , Number of controls: 447,052
    
  • Ancestry: European
  • Outcome: Atherosclerotic, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-b-1668
  • Sample size: 463,010 , Number of cases: 12,171 , Number of controls: 450,839
    
  • Ancestry: European
  • Outcome: Ischemic heart disease, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-d-I9_IHD
  • Sample size: 361,194 , Number of cases: 20,857 , Number of controls: 340,337
    
  • Ancestry: European
  • Outcome: Myocardial infarction, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-b-15829
  • Sample size: 462,933 , Number of cases: 10,616 , Number of controls: 452,317
    
  • Ancestry: European
  • Outcome: High blood pressure, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-b-14177
  • Sample size: 461,880 , Number of cases: 124,227 , Number of controls: 337,653
    
  • Ancestry: European

Data Preparation

1- Number of total SNPs in exposure: 12,321,875 SNPs

2- Number of Selected SNPs exposure: 44 SNPs

3- Number of total SNPs in outcome: 9,851,867 SNPs

4- Number of common variants between exposure and outcome: 34 SNPs

5- Number of SNPs after harmonization (action=2) = 33 SNPs

6- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 33 SNPs

7- Number of SNPs after removing those that have MAF < 0.01 = 33 SNPs

8- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 4 SNPs (rs429358, rs429358, rs56289821, and rs964184)

Checking weakness of the instruments

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   21.34   22.52   24.92   30.36   27.97   86.31

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

Initial MR analysis

id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
R5oDLI	pjYnfY	outcome	exposure	MR Egger	30	0.0047384	0.0034165	0.1764078
R5oDLI	pjYnfY	outcome	exposure	Weighted median	30	0.0015343	0.0012566	0.2220773
R5oDLI	pjYnfY	outcome	exposure	Inverse variance weighted	30	0.0017718	0.0009866	0.0725214
R5oDLI	pjYnfY	outcome	exposure	Simple mode	30	0.0015958	0.0026884	0.5573972
R5oDLI	pjYnfY	outcome	exposure	Weighted mode	30	0.0018886	0.0022402	0.4061129

Heterogeneity testing

id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
R5oDLI	pjYnfY	outcome	exposure	MR Egger	39.33190	28	0.0757304
R5oDLI	pjYnfY	outcome	exposure	Inverse variance weighted	40.48806	29	0.0762678

pleiotropy testing

id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
R5oDLI	pjYnfY	outcome	exposure	-0.0002567	0.000283	0.3720285

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate           Sd   T-stat
## 1 beta.exposure               Raw     0.001771766 0.0009865994 1.795831
## 2 beta.exposure Outlier-corrected              NA           NA       NA
##      P-value
## 1 0.08294832
## 2         NA
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 43.4608
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.085

MR analysis after excluding SNPs detected by MRPRESSO

id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
R5oDLI	pjYnfY	outcome	exposure	MR Egger	30	0.0047384	0.0034165	0.1764078
R5oDLI	pjYnfY	outcome	exposure	Weighted median	30	0.0015343	0.0012695	0.2268038
R5oDLI	pjYnfY	outcome	exposure	Inverse variance weighted	30	0.0017718	0.0009866	0.0725214
R5oDLI	pjYnfY	outcome	exposure	Simple mode	30	0.0015958	0.0026708	0.5548211
R5oDLI	pjYnfY	outcome	exposure	Weighted mode	30	0.0018886	0.0020249	0.3586752

Heterogeneity testing

id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
R5oDLI	pjYnfY	outcome	exposure	MR Egger	39.33190	28	0.0757304
R5oDLI	pjYnfY	outcome	exposure	Inverse variance weighted	40.48806	29	0.0762678

pleiotropy testing

id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
R5oDLI	pjYnfY	outcome	exposure	-0.0002567	0.000283	0.3720285

Radial test

## 
## Radial IVW
## 
##                     Estimate    Std.Error  t value   Pr(>|t|)
## Effect (Mod.2nd) 0.001771628 0.0009866445 1.795610 0.07255661
## Iterative        0.001771628 0.0009866445 1.795610 0.07255661
## Exact (FE)       0.001863303 0.0008373257 2.225302 0.02606098
## Exact (RE)       0.001838722 0.0010371981 1.772778 0.08677105
## 
## 
## Residual standard error: 1.179 on 29 degrees of freedom
## 
## F-statistic: 3.22 on 1 and 29 DF, p-value: 0.083
## Q-Statistic for heterogeneity: 40.28686 on 29 DF , p-value: 0.07935495
## 
##  No significant outliers 
## Number of iterations = 2

## [1] "No significant outliers"

MR analysis after excluding SNPs detected by MRPRESSO

id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
R5oDLI	pjYnfY	outcome	exposure	MR Egger	30	0.0047384	0.0034165	0.1764078
R5oDLI	pjYnfY	outcome	exposure	Weighted median	30	0.0015343	0.0012175	0.2075762
R5oDLI	pjYnfY	outcome	exposure	Inverse variance weighted	30	0.0017718	0.0009866	0.0725214
R5oDLI	pjYnfY	outcome	exposure	Simple mode	30	0.0015958	0.0026429	0.5506837
R5oDLI	pjYnfY	outcome	exposure	Weighted mode	30	0.0018886	0.0020965	0.3751116

Heterogeneity testing

id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
R5oDLI	pjYnfY	outcome	exposure	MR Egger	39.33190	28	0.0757304
R5oDLI	pjYnfY	outcome	exposure	Inverse variance weighted	40.48806	29	0.0762678

pleiotropy testing

id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
R5oDLI	pjYnfY	outcome	exposure	-0.0002567	0.000283	0.3720285

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Refernce

Run After deleting new outlier: Final Results:

MR analysis after deleting outliers

id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
R5oDLI	pjYnfY	outcome	exposure	MR Egger	27	0.0050723	0.0030927	0.1135130
R5oDLI	pjYnfY	outcome	exposure	Weighted median	27	0.0013964	0.0013041	0.2842530
R5oDLI	pjYnfY	outcome	exposure	Inverse variance weighted	27	0.0011386	0.0008867	0.1990822
R5oDLI	pjYnfY	outcome	exposure	Simple mode	27	0.0014728	0.0025957	0.5753012
R5oDLI	pjYnfY	outcome	exposure	Weighted mode	27	0.0017779	0.0022230	0.4310874

Heterogeneity testing

id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
R5oDLI	pjYnfY	outcome	exposure	MR Egger	21.26795	25	0.6775772
R5oDLI	pjYnfY	outcome	exposure	Inverse variance weighted	23.03059	26	0.6312158

pleiotropy testing

id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
R5oDLI	pjYnfY	outcome	exposure	-0.0003332	0.000251	0.1962922

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 27 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     IVW    0.001     0.001 -0.001, 0.003   0.199
## ------------------------------------------------------------------
## Residual standard error =  0.941 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 23.0306 on 26 degrees of freedom, (p-value = 0.6312). I^2 = 0.0%.

##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.001     0.001  -0.001 0.004   0.339
##            Weighted median    0.001     0.001  -0.001 0.004   0.269
##  Penalized weighted median    0.001     0.001  -0.001 0.004   0.269
##                                                                    
##                        IVW    0.001     0.001  -0.001 0.003   0.199
##              Penalized IVW    0.001     0.001  -0.001 0.003   0.199
##                 Robust IVW    0.001     0.001  -0.001 0.003   0.187
##       Penalized robust IVW    0.001     0.001  -0.001 0.003   0.187
##                                                                    
##                   MR-Egger    0.005     0.003  -0.001 0.011   0.101
##                (intercept)    0.000     0.000  -0.001 0.000   0.184
##         Penalized MR-Egger    0.005     0.003  -0.001 0.011   0.101
##                (intercept)    0.000     0.000  -0.001 0.000   0.184
##            Robust MR-Egger    0.005     0.002   0.001 0.010   0.029
##                (intercept)    0.000     0.000  -0.001 0.000   0.096
##  Penalized robust MR-Egger    0.005     0.002   0.001 0.010   0.029
##                (intercept)    0.000     0.000  -0.001 0.000   0.096

id.exposure	id.outcome	exposure	outcome	snp_r2.exposure	snp_r2.outcome	correct_causal_direction	steiger_pval
R5oDLI	pjYnfY	exposure	outcome	0.0019071	4.99e-05	TRUE	0

## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] 0.001171598
## 
## $beta.se
## [1] 0.0009206665
## 
## $beta.p.value
## [1] 0.2031764
## 
## $naive.se
## [1] 0.0009051455
## 
## $chi.sq.test
## [1] 22.98271

##   over.dispersion loss.function    beta.hat      beta.se
## 1           FALSE            l2 0.001171598 0.0009206665
## 2           FALSE         huber 0.001259075 0.0009449070
## 3           FALSE         tukey 0.001207582 0.0009447155
## 4            TRUE            l2 0.001173555 0.0009415467
## 5            TRUE         huber 0.001249328 0.0009449544
## 6            TRUE         tukey 0.001205204 0.0009447884

## 
## MR-Lasso method 
## 
## Number of variants : 27 
## Number of valid instruments : 27 
## Tuning parameter : 0.3447026 
## ------------------------------------------------------------------
##  Exposure Estimate Std Error  95% CI       p-value
##  exposure    0.001     0.001 -0.001, 0.003   0.199
## ------------------------------------------------------------------

## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  27 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue         95% CI
##  cML-MA-BIC    0.001 0.001  0.193 [-0.001,0.003]
## ------------------------------------------------------------------

## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 27 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value Condition
##    dIVW    0.001     0.001 -0.001, 0.003   0.200   151.059
## ------------------------------------------------------------------

## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 27 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE    0.002     0.002 -0.003, 0.006   0.424
## ------------------------------------------------------------------

[HTN]

Introduction

• Title: Investigating the causality between Monounsaturated Fatty Acids on Cardiovascular Disease

  • Exposure: Monounsaturated Fatty Acids, Data downloaded from IEU OpenGWAS project Database | ID: ukb-b-8468
  • Sample size: 461,880
  • Outcome: Angina, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-b-8468
  • Sample size: 461,880 , Number of cases: 14,828 , Number of controls: 447,052
    
  • Ancestry: European
  • Outcome: Atherosclerotic, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-b-1668
  • Sample size: 463,010 , Number of cases: 12,171 , Number of controls: 450,839
    
  • Ancestry: European
  • Outcome: Ischemic heart disease, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-d-I9_IHD
  • Sample size: 361,194 , Number of cases: 20,857 , Number of controls: 340,337
    
  • Ancestry: European
  • Outcome: Myocardial infarction, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-b-15829
  • Sample size: 462,933 , Number of cases: 10,616 , Number of controls: 452,317
    
  • Ancestry: European
  • Outcome: High blood pressure, Data downloaded from IEU OpenGWAS project Database | GWAS ID: ukb-b-14177
  • Sample size: 461,880 , Number of cases: 124,227 , Number of controls: 337,653
    
  • Ancestry: European

Data Preparation

1- Number of total SNPs in exposure: 12,321,875 SNPs

2- Number of Selected SNPs exposure: 44 SNPs

3- Number of total SNPs in outcome: 9,851,867 SNPs

4- Number of common variants between exposure and outcome: 40 SNPs

5- Number of SNPs after harmonization (action=2) = 40 SNPs

6- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 40 SNPs

7- Number of SNPs after removing those that have MAF < 0.01 = 40 SNPs

8- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 4 SNPs (rs1554903 and rs429358)

Checking weakness of the instruments

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   21.29   22.26   24.01   30.47   28.10   86.31

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

Initial MR analysis

id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
fAazZl	uqi37M	outcome	exposure	MR Egger	37	0.0063402	0.0092623	0.4981580
fAazZl	uqi37M	outcome	exposure	Weighted median	37	0.0087999	0.0033911	0.0094601
fAazZl	uqi37M	outcome	exposure	Inverse variance weighted	37	0.0064439	0.0033897	0.0572976
fAazZl	uqi37M	outcome	exposure	Simple mode	37	0.0108348	0.0076165	0.1634740
fAazZl	uqi37M	outcome	exposure	Weighted mode	37	0.0102740	0.0060846	0.0999577

Heterogeneity testing

id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
fAazZl	uqi37M	outcome	exposure	MR Egger	86.47991	35	3.0e-06
fAazZl	uqi37M	outcome	exposure	Inverse variance weighted	86.48027	36	4.9e-06

pleiotropy testing

id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
fAazZl	uqi37M	outcome	exposure	1.01e-05	0.000837	0.9904535

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate          Sd   T-stat
## 1 beta.exposure               Raw     0.006443858 0.003389660 1.901034
## 2 beta.exposure Outlier-corrected     0.006519442 0.003024166 2.155782
##      P-value
## 1 0.06532639
## 2 0.03826639
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 91.98975
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] "<0.001"
## 
## 
## $`MR-PRESSO results`$`Outlier Test`
##          RSSobs Pvalue
## 1  4.490365e-08      1
## 2  1.714504e-06      1
## 3  2.638681e-06      1
## 4  4.078232e-05      1
## 5  2.091918e-08      1
## 6  9.352604e-07      1
## 7  1.025229e-06      1
## 8  5.783611e-06   0.37
## 9  9.252651e-07      1
## 10 6.287315e-05      1
## 11 3.280347e-08      1
## 12 2.601647e-07      1
## 13 8.342274e-07      1
## 14 9.509238e-07      1
## 15 4.911202e-06      1
## 16 3.216041e-06      1
## 17 2.075340e-07      1
## 18 1.944242e-07      1
## 19 3.563012e-08      1
## 20 5.965255e-08      1
## 21 4.735677e-05  0.444
## 22 8.391620e-07      1
## 23 3.322211e-06      1
## 24 2.996330e-05      1
## 25 4.582138e-08      1
## 26 3.658378e-06      1
## 27 2.282894e-06      1
## 28 2.723694e-05 <0.037
## 29 4.140334e-06  0.999
## 30 2.527450e-05      1
## 31 1.641552e-05      1
## 32 1.591477e-08      1
## 33 3.129629e-06      1
## 34 2.413713e-07      1
## 35 4.193323e-05 <0.037
## 36 3.043937e-06      1
## 37 1.444488e-05  0.481
## 
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 28 35
## 
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure 
##     -1.159357 
## 
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.968

MR analysis after excluding SNPs detected by MRPRESSO

id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
fAazZl	uqi37M	outcome	exposure	MR Egger	36	0.0062364	0.0096263	0.5214344
fAazZl	uqi37M	outcome	exposure	Weighted median	36	0.0089921	0.0037121	0.0154201
fAazZl	uqi37M	outcome	exposure	Inverse variance weighted	36	0.0064117	0.0035025	0.0671570
fAazZl	uqi37M	outcome	exposure	Simple mode	36	0.0116985	0.0077081	0.1380716
fAazZl	uqi37M	outcome	exposure	Weighted mode	36	0.0108538	0.0062039	0.0889681

Heterogeneity testing

id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
fAazZl	uqi37M	outcome	exposure	MR Egger	86.47362	34	1.9e-06
fAazZl	uqi37M	outcome	exposure	Inverse variance weighted	86.47460	35	3.0e-06

pleiotropy testing

id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
fAazZl	uqi37M	outcome	exposure	1.69e-05	0.00086	0.9844792

Radial test

## 
## Radial IVW
## 
##                     Estimate   Std.Error  t value    Pr(>|t|)
## Effect (Mod.2nd) 0.006446794 0.003390225 1.901583 0.057225701
## Iterative        0.006446794 0.003390225 1.901583 0.057225701
## Exact (FE)       0.006990333 0.002197330 3.181285 0.001466233
## Exact (RE)       0.006675048 0.003642112 1.832741 0.075122185
## 
## 
## Residual standard error: 1.544 on 36 degrees of freedom
## 
## F-statistic: 3.62 on 1 and 36 DF, p-value: 0.0653
## Q-Statistic for heterogeneity: 85.81857 on 36 DF , p-value: 5.975782e-06
## 
##  Outliers detected 
## Number of iterations = 2

##         SNP Q_statistic      p.value
## 1 rs7123454     12.7942 0.0003476959
## 2 rs8107974     13.0189 0.0003083633

MR analysis after excluding SNPs detected by MRPRESSO

id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
fAazZl	uqi37M	outcome	exposure	MR Egger	35	0.0082727	0.0082800	0.3250118
fAazZl	uqi37M	outcome	exposure	Weighted median	35	0.0088240	0.0035685	0.0134082
fAazZl	uqi37M	outcome	exposure	Inverse variance weighted	35	0.0065194	0.0030242	0.0311007
fAazZl	uqi37M	outcome	exposure	Simple mode	35	0.0108836	0.0072360	0.1417916
fAazZl	uqi37M	outcome	exposure	Weighted mode	35	0.0099036	0.0061075	0.1141422

Heterogeneity testing

id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
fAazZl	uqi37M	outcome	exposure	MR Egger	60.37413	33	0.0025134
fAazZl	uqi37M	outcome	exposure	Inverse variance weighted	60.46920	34	0.0034450

pleiotropy testing

id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
fAazZl	uqi37M	outcome	exposure	-0.0001673	0.0007338	0.8210859

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Refernce

Run After deleting new outlier: Final Results:

MR analysis after deleting outliers

id.exposure	id.outcome	outcome	exposure	method	nsnp	b	se	pval
fAazZl	uqi37M	outcome	exposure	MR Egger	34	0.0026933	0.0082760	0.7469735
fAazZl	uqi37M	outcome	exposure	Weighted median	34	0.0082770	0.0035509	0.0197573
fAazZl	uqi37M	outcome	exposure	Inverse variance weighted	34	0.0048753	0.0029682	0.1004810
fAazZl	uqi37M	outcome	exposure	Simple mode	34	0.0107320	0.0068367	0.1260113
fAazZl	uqi37M	outcome	exposure	Weighted mode	34	0.0097417	0.0054812	0.0847364

Heterogeneity testing

id.exposure	id.outcome	outcome	exposure	method	Q	Q_df	Q_pval
fAazZl	uqi37M	outcome	exposure	MR Egger	52.74506	32	0.0119122
fAazZl	uqi37M	outcome	exposure	Inverse variance weighted	52.87712	33	0.0155079

pleiotropy testing

id.exposure	id.outcome	outcome	exposure	egger_intercept	se	pval
fAazZl	uqi37M	outcome	exposure	0.0002031	0.0007175	0.7789617

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 34 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     IVW    0.005     0.003 -0.001, 0.011   0.100
## ------------------------------------------------------------------
## Residual standard error =  1.266 
## Heterogeneity test statistic (Cochran's Q) = 52.8771 on 33 degrees of freedom, (p-value = 0.0155). I^2 = 37.6%.

##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.008     0.004   0.001 0.015   0.030
##            Weighted median    0.009     0.004   0.001 0.016   0.019
##  Penalized weighted median    0.009     0.004   0.002 0.016   0.014
##                                                                    
##                        IVW    0.005     0.003  -0.001 0.011   0.100
##              Penalized IVW    0.005     0.003  -0.001 0.011   0.100
##                 Robust IVW    0.005     0.003  -0.001 0.011   0.090
##       Penalized robust IVW    0.005     0.003  -0.001 0.011   0.090
##                                                                    
##                   MR-Egger    0.003     0.008  -0.014 0.019   0.745
##                (intercept)    0.000     0.001  -0.001 0.002   0.777
##         Penalized MR-Egger    0.003     0.008  -0.014 0.019   0.745
##                (intercept)    0.000     0.001  -0.001 0.002   0.777
##            Robust MR-Egger    0.003     0.011  -0.018 0.024   0.775
##                (intercept)    0.000     0.001  -0.002 0.002   0.836
##  Penalized robust MR-Egger    0.003     0.011  -0.018 0.024   0.775
##                (intercept)    0.000     0.001  -0.002 0.002   0.836

id.exposure	id.outcome	exposure	outcome	snp_r2.exposure	snp_r2.outcome	correct_causal_direction	steiger_pval
fAazZl	uqi37M	exposure	outcome	0.0022824	0.0001158	TRUE	0

## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] 0.00515672
## 
## $beta.se
## [1] 0.002410337
## 
## $beta.p.value
## [1] 0.03240175
## 
## $naive.se
## [1] 0.002368768
## 
## $chi.sq.test
## [1] 52.62634

##   over.dispersion loss.function    beta.hat     beta.se
## 1           FALSE            l2 0.005156720 0.002410337
## 2           FALSE         huber 0.006313638 0.002479360
## 3           FALSE         tukey 0.006002630 0.002477515
## 4            TRUE            l2 0.003985094 0.003767475
## 5            TRUE         huber 0.004148444 0.004721347
## 6            TRUE         tukey 0.004112417 0.004479062

## 
## MR-Lasso method 
## 
## Number of variants : 34 
## Number of valid instruments : 27 
## Tuning parameter : 0.3036984 
## ------------------------------------------------------------------
##  Exposure Estimate Std Error 95% CI       p-value
##  exposure    0.008     0.003 0.003, 0.013   0.003
## ------------------------------------------------------------------

## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  34 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.005 0.002  0.034 [0.000,0.010]
## ------------------------------------------------------------------

## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 34 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value Condition
##    dIVW    0.005     0.003 -0.001, 0.011   0.098   160.809
## ------------------------------------------------------------------

## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 34 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE    0.010     0.006 -0.002, 0.021   0.102
## ------------------------------------------------------------------